Finite Math Examples

$x + y^{2} = 0$ , $5 x + 6 y^{2} = 64$

Step 1

Subtract $y^{2}$ from both sides of the equation.

$x = - y^{2}$

$5 x + 6 y^{2} = 64$

Step 2

Replace all occurrences of $x$ with $- y^{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x + 6 y^{2} = 64$ with $- y^{2}$ .

$5 (- y^{2}) + 6 y^{2} = 64$

$x = - y^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (- y^{2}) + 6 y^{2}$ .

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Step 2.2.1.1

Multiply $- 1$ by $5$ .

$- 5 y^{2} + 6 y^{2} = 64$

$x = - y^{2}$

Step 2.2.1.2

Add $- 5 y^{2}$ and $6 y^{2}$ .

$y^{2} = 64$

$x = - y^{2}$

$y^{2} = 64$

$x = - y^{2}$

$y^{2} = 64$

$x = - y^{2}$

$y^{2} = 64$

$x = - y^{2}$

Step 3

Solve for $y$ in $y^{2} = 64$ .

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Step 3.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{64}$

$x = - y^{2}$

Step 3.2

Simplify $\pm \sqrt{64}$ .

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Step 3.2.1

Rewrite $64$ as $8^{2}$ .

$y = \pm \sqrt{8^{2}}$

$x = - y^{2}$

Step 3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 8$

$x = - y^{2}$

$y = \pm 8$

$x = - y^{2}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 8$

$x = - y^{2}$

Step 3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 8$

$x = - y^{2}$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = 8, - 8$

$x = - y^{2}$

$y = 8, - 8$

$x = - y^{2}$

$y = 8, - 8$

$x = - y^{2}$

Step 4

Replace all occurrences of $y$ with $8$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - y^{2}$ with $8$ .

$x = - {(8)}^{2}$

$y = 8$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- {(8)}^{2}$ .

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Step 4.2.1.1

Raise $8$ to the power of $2$ .

$x = - 1 \cdot 64$

$y = 8$

Step 4.2.1.2

Multiply $- 1$ by $64$ .

$x = - 64$

$y = 8$

$x = - 64$

$y = 8$

$x = - 64$

$y = 8$

$x = - 64$

$y = 8$

Step 5

Replace all occurrences of $y$ with $- 8$ in each equation.

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Step 5.1

Replace all occurrences of $y$ in $x = - y^{2}$ with $- 8$ .

$x = - {(- 8)}^{2}$

$y = - 8$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- {(- 8)}^{2}$ .

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Step 5.2.1.1

Raise $- 8$ to the power of $2$ .

$x = - 1 \cdot 64$

$y = - 8$

Step 5.2.1.2

Multiply $- 1$ by $64$ .

$x = - 64$

$y = - 8$

$x = - 64$

$y = - 8$

$x = - 64$

$y = - 8$

$x = - 64$

$y = - 8$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 64, 8)$

$(- 64, - 8)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 64, 8), (- 64, - 8)$

Equation Form:

$x = - 64, y = 8$

$x = - 64, y = - 8$

Step 8